Averaged run-and-tumble walks
CNR-IPCF, UOS Roma c/o Dipartimento di Fisica, Università “Sapienza” - I-00185 Roma, Italy, EU
Received: 20 February 2013
Accepted: 3 April 2013
A random walk consisting of a run phase at constant speed interrupted by tumble events is analyzed and analytically solved for arbitrary time distributions. A general expression is given for the Laplace-Fourier transform of the probability density function and for the mean square displacement averaging over initial conditions. Run-and-tumble bacteria and Lévy walks are considered as particular cases. The effects of an underlying Brownian noise are also discussed. Derived expressions can be used for a direct comparison with experimentally measured quantities.
PACS: 05.40.Fb – Random walks and Levy flights / 02.50.Ey – Stochastic processes / 87.17.Jj – Cell locomotion, chemotaxis
© EPLA, 2013